I should really know this but i dont.
Thanks
brian73

Refers to a very small portion of a circle. The term is usually considered to mean that a rifle shooting sub-MOA, ie Minute of Angle..means that it shoots groups of UNDER 1" at 100 yds, from a rest. Anybody else got a more technically correct definition? That's the best I can do..and I can't even see that well...LOL

You're right. I'll add that MOA is defined as 1/60th of a degree, hence the name "minute". Just imagine a tringle with two sides 100yds long and the third side 1" long. The angle between the two long sides is about 1 MOA.

thanks guys,  I had a hunch it was around a 1" group, but just couldn't figure out what MOA stood for.

brian73

As Fred said, MOA is Minute Of Angle.  A minute is 1/60th of a degree.  The practical application of this with reference to shooting is that one minute is almost exactly one inch at 100 yards (or 3600 inches).  If I'm thinking clearly and my math is right, sin(1/60 degree)*3600 inches = 1.047... inches.

Yeah, it's an astonomical or navigational term, minute, that is.  When you extend your arm your fist covers about 10 degrees (useful for spotting stars, ie. star xyz is 15 degrees below the north star, fist and a 1/2 below).  Each degree is divided into 60 minutes.

So, if you hold our your fist out at the shooting range and divide by knuckles and thumb (1/5th each), you will see that each knuckle covers about 2 degrees or 120 minutes.  That's about 10 feet at 100 yards...

BTW, astronomers commonly use "seconds of angle" which are 1/60 of a MOA, reffered to as "arcseconds". They call MOA "arcminutes".

Wrong.  R(Radius)=100 yards or 3600"
3.14(pi)x 3600"(R)= 11304"
11304" divided by 360(degrees)=31.4" per degree
31.4" divided by 60(minutes)=.523333333333".....

Now, imagine a cone extending from the muzzle.  At 100 yards the cone has a base diameter of 1.046".  The center point of the cone base is the perfect shot, bullseye.  If the firearm keeps shots inside this cone, no point of impact deviates more than 1 MOA from the center.  The center in reality, is the center of your group. Groups are measured center to center [b]of the two farthest holes[/b] in the group.  Those hole centers can be no farther than .523" from the [b]center of the group[/b] to be subMOA.    

David M - Qwijibo is right. Your error is the circumference is 2*pi*r not pi*r. So 1 MOA is 1.047 inches @ 100yds. But your conclusion is correct, since .523 radius group=1.047 diameter group.

WHAT??   Well ##$%$##$#^#^^#^#$%!!!!!                                        [:(!]

You are of course, both right.  Circumferance=Diameter x pi.  Thank you, MadMatt.  My apologies Qwijibo.  

Far be it for me to take a hard line position on this thread.  But Metric?  I thought all metric was based on numbers of 10.  Degrees and such were thought up long ago by the Greeks, or so I thought.  Way before metrics.
I sure do agree, MOA is relative to the distance of the shot.  The angle widens proportionately.

Just as I thought.  I'm not gloating though.  You can bet on that!

Accepted Units.
For practical reasons a number of non-metric units are accepted for use. These include units
of time (minute, hour, etc.), units of plane angle (degree, etc.), and a few units for special a few units for special applications, such as the nautical mile, used in navigation. Section 5 includes accepted units and shows their areas of application. These units may be used in full compliance with the provisions of the amended Metric Conversion Act, EO 12770, and the Federal Register Notice, "Metric System of Measurement; Interpretation of the International
System of Units for the United States" (55 F.R. 52242, Dec. 20, 1990).

Correct, MOA doesn't have anything to do with yards, or I might add, the metric system. To phrase it precisely, a 1" circle subtends an angle of 1 MOA at 100yds. But at the shootin' range 1 MOA = 1" @ 100yds. = 2" @ 200yds. etc.

The distance from the North Pole to the equator, 10,000,000 meters.  Now, I'm gloating![8D]

Or, is it 1,000,000 meters?  Now, I've done forgot!  No longer gloating.

The meter was originally defined as one ten millionth of the distance between the north pole and the equator, along the meridian through Paris. No wonder Americans hate the metric system.

ok ok, a 1" circle @ 100yds subtends an angle of 1 MOA, or add a comma to my previous statement.

You asked a question and you got a answer. and a half. Thanks guys we all needed brushing up on MOA 101.

Lets make this a little simple for those who are trying to make since of this in terms of a rifles accuracy.

If a rifle is capable of 1 MOA  that means it will theoretically (sp?) shoot a 1.04 inch group at 100 yards, a 5.2 inch group at 500 yards, a 10.4 inch group at 1000 yards, and so on...

Plain as mud? I thought so.

Jake

Sorry for posting the whole thing guys. Maybe this will settle the dispute.

XII. Accuracy
C. Miscellaneous
4. What is a Minute of Angle (MOA)?
by Robert W. Current ([email protected]) and Trevor M. Riedemann ([email protected]) .
It is a measurement of angle, a subdivision of a degree. There are 360 degrees in a full circle

4 quadrants = 1 circle
90 degrees = 1 quadrant
60 minutes = 1 degree
60 seconds = 1 minute
21,600 minutes = 1 circle

So they are all just measurements of an angle, should be listed in any fact finder or such.

The reason it is so widely used in the shooting sports is because if you measure an angle of one minute the lines almost run parallel at short distances, but at long distances you can see them separate. And quite conveniently they separate to 1 inch apart when you get 100 yards from the point they cross. That works out great for measuring rifle accuracy (in an idealized situation, no wind, ...):

Shots spread at an angle, increasing group size as distance from the target increases.

Diagram 1



"M" is the muzzle and "d" is the distance to the target, now it is easy to see the closer you are to the Target, the more likely you are to hit it (we all know that, at least intuitively) and it can be seen it is some function of an angle. That is why accuracy is ideally measured in angles not just shot spread.

So, if you have a 1 Minute of Angle (1 MOA) rifle, you can expect about one inch groups at 100 yards, 2 inch groups at 200 yards, 3 inch groups at 300 yards.

To explain this if full detail requires the use of trigonometry/geometry:

Diagram 2



At a distance of 100 yards from the target, length "d" on the diagram, you shoot a group that measures one inch, segment "C" on the diagram.

Then:
tan(q/2) = C/2d
(look at the addendum below to see how this is found)

Solving for theta
q = 2 tan-1(C/2d)

For C = 1 inch
d = 100 yards = 3600 inches
q = 0.0159155 degrees = 0.9549 arcmin

Alternatively this can be made by an approximation:
S = Rq
where q is in radians solve for theta
q = S/R
S is approximately equal to C (1.0000004" ~ 1")

R is approximately equal to d (100.000001 yards ~ 100 yards)
q = C/d = 1 inch/3600 inch = 0.00027777 radians = 0.9549 arcmin

So, your one inch group at 100 yards is really 0.95 MOA group!

Want to go into more detail? Well a degree is symbolized by a little o above and to the right of the number, a minute is symbolized by a single apostrophe (') and a second is abbreviated with a double apostrophe ("). You know what that means? I could say I shot a 1' group (a "one minute" group), and it could mean I shot a group that was 0.95 inches at 100 yards, or even a 1.8 inch group at 200 yards. This use of the symbols is really one of my pet peeves, that I never really rant about, I just let people sound silly and laugh to myself later. I shot a 1" group. Wow, did I read that article right, he said 1" that is one second right? It has to be, he didn't say 1 inch at a 100 yard distance, he didn't even mention distance, so he must be reporting accuracy in MOA, and that would work out to be 1/60 (one sixtieth) of an inch at 100 yards. Man those guys are so good, I must really suck, I will never be able to shoot that well.

But, even this all seems to be an ideal way of measuring things for shooting, you have to keep in mind that the real world is rarely ideal. You really have to take a few more things into a

I think I'll just settle for "right between the eyes" at 100 yards.

Thats way to complicated for me. Hows your ar shoot...1" groups...Great! Thats all i need to know. My head is so full of useless information that if i tried to remeber all those formulas i would have to forget something. Like my wifes name..

h-d man, be sure to qualify that with a range.  1" at 100yd is good.  1" at 5yd is horrible. =)

Wilson,

And ya'all are doing a mighty fine job of it!

Thanks for the math lesson.

I agree, but it is nice to see this kind of detailed talk on occasion. Actually I found the information exchange to be quite informative and refreshing.

Now I know why the term (More information than I needed to know)is used.